VarianceGammaCf

Variance-Gamma characteristic function of the log-return. VG is Brownian motion with drift theta and volatility sigma evaluated at a Gamma-distributed business time with unit mean rate and variance nu:

phi(u) = exp( i u (r + omega) T ) (1 - i u theta nu + sigma^2 nu u^2 / 2)^{-T/nu}
omega  = (1/nu) ln(1 - theta nu - sigma^2 nu / 2)     (martingale correction)

As nu -> 0 the Gamma time concentrates and VG -> Black-Scholes with volatility sigma. This is also the closed-form pricing route for the VG model that the F7 Monte-Carlo step block deferred.